Understanding the Relationship between Negative Angles and Tangent Function

[Jerbearrrrrr]

This isn't my problem, it's a friends. I'll post my explanation and you tell me what's wrong with it cause she still doesn't understand. Thanks.

[PLAIN][PLAIN]http://img43.imageshack.us/img43/3020/32112328.png
Find tan(theta), given the coordinates of the arrow.

I said
"well tanx = tan(x-180) by looking at the tan graph, which repeats every 180 So we can add 180 degrees to that angle, and take the tan of that instead"
(picture)
"the tan of that is op/adj which is easier
If the original vector was (a,b)
Then this vector is going to be (-a,-b)"
(picture)
"tan of ( ) = tan of ( )
so if the first angle is -120, then the second is -120+180=60
and tan(-120) = tan(60)"

--------
This is the conversation if you're curious...sigh. Don't have to read this bit, but I would kind of like to know how to handle this situation.


B:so if it was like
[PLAIN][PLAIN]http://img43.imageshack.us/img43/3020/32112328.png

and it was like what's tan theta so do i just do tan of the small triangle thing then + pi/2?

A:well tanx = tan(x-180) by looking at the tan graph, which repeats every 180 So we can add 180 degrees to that angle, and take the tan of that instead

B:too confusing don't understand what youre saying

A:
[PLAIN][PLAIN]http://img168.imageshack.us/img168/2210/79577809.png
angle there is x+180

B:but its not asking for that angle

A:Tan (that angle) is tan(theta)
they are the same

B: so i was supposed to move the graph sideways or what?

A:Yeah

B:..?

http://img43.imageshack.us/img43/3898/11665177.png
is not the same as
http://img43.imageshack.us/img43/1285/16166454.png

A:the tangent of both angles are the same though

B:the angles are DIFFERENT
****
i don't know why i ask you
forget it

A:Yes, the angles are different, but tan(angle1) = tan(angle2)

B: obviously if you say it once and i don't get it
if you say the same thing again
i am still not going to get it
(insert more irrelevant conversation)

A:The quickest explanation is that the tan graph repeats every 180, hence tan{x}=tan{x+180}

B:what does that have to do
WITH ANYTHING?

A: it means if we want tan{x} (theta=x for now) but x is hard to deal with, we can add 180 as many times as we want, and take the tan{ } of that instead.

Bk
again I am going to ask you
what does that have to do with anything
ok if the component is (A,B) then what is the answer

A:[PLAIN][PLAIN]http://img168.imageshack.us/img168/2210/79577809.png
And the tan of that is op/adj which is easier
If the original vector was (a,b)
Then this vector is going to be (-a,-b)
so b/a

B: ok so basically what i got out of what you said is
http://img168.imageshack.us/img168/5272/12495044.png
which i already know is wrong so thanks anyway

A:tan of ( ) = tan of ( )
so if the first angle is -120, then the second is -120+180=60
and tan(-120) = tan(60)

The rest is more swearing than explanation so I won't paste it in.

 

[Mentallic]

omg this was hilarious!

I know how frustrated you must feel, especially

i don't know why i ask you
forget it

then the student goes and asks someone else. This other person gives a half-assed answer such as "just put it in the calculator" and then student B exclaims with "ooh now I get it"... Now THAT is frustrating

I have learned to just give up and direct them to the teachers, but it looks like you still want guidance to keep trying to help your friend. The best I can say is that you should get her to draw the graph of tanx in a large domain, then ask her to say show approximately where -120^o is and finally what tan(-120^o) is. Now do the same for 60^o, maybe this will make it click for her? If it does, then you can take that big step of translating the graph into the quadrant system

 

[Simon.T]

Tee hee.

You may want to explain it using a plot of tangent function compared to say, the sin function. It will be quite clear to see that the function (for tan) repeats every 180deg.

You can them demonstrate it by putting examples into a calculator... tan(60) and tan(240) for example and getting the same answer.